Spectral theory of Dirac system on time scales

Abstract

Boundary value problem on time scales is fairly a new subject and has great importance in mathematics. In this study, we explore an eigenvalue problem for Dirac system with separated boundary conditions on an arbitrary time scale T. Recent results in the literature about spectral theory of classical Dirac system as orthogonality of eigenfunctions and simplicity of the eigenvalues are generalized and improved. Furthermore, some eigenfunction estimates of the first and second canonic forms for Dirac system are established on T. These results will provide a significant contribution to the development of the spectral theory on time scales.